We compute the one-loop QCD amplitudes for the decay of an off-shell v
ector boson with vector couplings into a quark-antiquark pair accompan
ied by two gluons keeping, for the first time, all orders in the numbe
r of colours. Together with previous work this completes the calculati
on of the necessary one-loop amplitudes needed for the calculation of
the next-to-leading order O(alpha(s)(3)) corrections to four jet produ
ction in electron-positron annihilation, the production of a gauge bos
on accompanied by two jets in hadron-hadron collisions and three jet p
roduction in deep inelastic scattering. (C) 1997 Elsevier Science B.V.